Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Tight lower bounds for the size of epsilon-nets
Proceedings of the twenty-seventh annual symposium on Computational geometry
Cover-decomposition and polychromatic numbers
ESA'11 Proceedings of the 19th European conference on Algorithms
Polychromatic coloring for half-planes
Journal of Combinatorial Theory Series A
Maximizing network lifetime on the line with adjustable sensing ranges
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
A better approximation ratio and an IP formulation for a sensor cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Coloring planar homothets and three-dimensional hypergraphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Changing of the guards: strip cover with duty cycling
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Brief announcement: set it and forget it - approximating the set once strip cover problem
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Coloring planar homothets and three-dimensional hypergraphs
Computational Geometry: Theory and Applications
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We show that a k-fold covering using translates of an arbitrary convex polygon can be decomposed into Omega(k) covers (using an efficient algorithm). We generalize this result to obtain a constant factor approximation to the sensor cover problem where the ranges of the sensors are translates of a given convex polygon. The crucial ingredient in this generalization is a constant factor approximation algorithm for a one-dimensional version of the sensor cover problem, called the Restricted Strip Cover (RSC) problem, where sensors are intervals of possibly different lengths. Our algorithm for RSC improves on the previous O(log log log n) approximation.